Answer

Verified

452.4k+ views

Hint: - Here, we use bisector formulas to find midpoints.

Let \[{\text{A(}} - {\text{6,8)}}\] and \[{\text{B(8,}} - {\text{6)}}\] and \[{\text{P,Q,R}}\] divides \[{\text{AB}}\] in four equal parts \[{\text{Q}}\] divides \[{\text{AB}}\] in \[{\text{1:1}}\],so \[{\text{Q}}\] is the midpoint of \[{\text{AB}}\].

So coordinates of \[{\text{Q}}\] are \[\dfrac{{ - {\text{6 + 8}}}}{2}{\text{,}}\dfrac{{{\text{8}} - {\text{6}}}}{2}\]

\[ \Rightarrow {\text{Q}}(1,1)\]

Similarly ${\text{P}}$ is the midpoint of \[{\text{AQ}}\]

So coordinates of ${\text{P }}$ are \[\dfrac{{ - {\text{6 + 1}}}}{2},\dfrac{{8+1}}{2}\]

\[ \Rightarrow {\text{P}}\left( { - \dfrac{5}{2},\dfrac{9}{2}} \right)\]

And now \[{\text{R }}\] is the midpoint of ${\text{QB}}$

So coordinates of \[{\text{R}}\] are \[\dfrac{{1 + 8}}{2},\dfrac{{1 - 6}}{2}\]

\[ \Rightarrow {\text{R }}\left( {\dfrac{9}{2},\dfrac{{ - 5}}{2}} \right)\]

The points which divide the line in four equal parts are \[\left( { - \dfrac{5}{2},\dfrac{9}{2}} \right);(1,1);\left( {\dfrac{9}{2},\dfrac{{ - 5}}{2}} \right)\]

Note:-Whenever we face such types of questions it is better to denote the coordinate by letter and then bisect the first line and after that bisect that line. Which are made by the bisector of the first line.

Let \[{\text{A(}} - {\text{6,8)}}\] and \[{\text{B(8,}} - {\text{6)}}\] and \[{\text{P,Q,R}}\] divides \[{\text{AB}}\] in four equal parts \[{\text{Q}}\] divides \[{\text{AB}}\] in \[{\text{1:1}}\],so \[{\text{Q}}\] is the midpoint of \[{\text{AB}}\].

So coordinates of \[{\text{Q}}\] are \[\dfrac{{ - {\text{6 + 8}}}}{2}{\text{,}}\dfrac{{{\text{8}} - {\text{6}}}}{2}\]

\[ \Rightarrow {\text{Q}}(1,1)\]

Similarly ${\text{P}}$ is the midpoint of \[{\text{AQ}}\]

So coordinates of ${\text{P }}$ are \[\dfrac{{ - {\text{6 + 1}}}}{2},\dfrac{{8+1}}{2}\]

\[ \Rightarrow {\text{P}}\left( { - \dfrac{5}{2},\dfrac{9}{2}} \right)\]

And now \[{\text{R }}\] is the midpoint of ${\text{QB}}$

So coordinates of \[{\text{R}}\] are \[\dfrac{{1 + 8}}{2},\dfrac{{1 - 6}}{2}\]

\[ \Rightarrow {\text{R }}\left( {\dfrac{9}{2},\dfrac{{ - 5}}{2}} \right)\]

The points which divide the line in four equal parts are \[\left( { - \dfrac{5}{2},\dfrac{9}{2}} \right);(1,1);\left( {\dfrac{9}{2},\dfrac{{ - 5}}{2}} \right)\]

Note:-Whenever we face such types of questions it is better to denote the coordinate by letter and then bisect the first line and after that bisect that line. Which are made by the bisector of the first line.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

How many crores make 10 million class 7 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths